Please help.I can't use the law of momentum when the objects are collided.

1. The problem statement, all variables and given/known data
Now,I am making the real game.The user can control the bat to hit the ball.
Please look at this picture.

Assume m2 is the bat and m1 is the ball
The bat has its angle and its velocity vector(x,y).
I want to find final velocity of the ball. I know the vector(x,y) of v1,v2 ,angle of the bat.
I can't use this formular :
m1v1+m2v2 = m1v1f+m2v2f and the formula for the conservation of kinetic energy
(v1f is the final velocity of the ball)
because the picture left and right have the same value of v1,v2.so they will have the same v1f.

2. Relevant equations

3. The attempt at a solution
I try to find the normal of the bat and calculate it .follow by this picture.
Sorry,The Picture is not correct; I use this formular : v1f = vv+v2

But it's not good
How can I find the final velocity of the ball?
Please give me some solution.

If the bat is moving freely (nothing holding one end) and the middle of the bat hits the ball, and the bat & ball have no relative velocity in the direction parallel to its surface, then the solution is an easy one dimensional momentum problem, where the only direction that matters is the one perpendicular to the bat. If there is a component of velocity parallel to the bat, then you have to do something with the "grip" or friction between bat and ball to figure out what should happen in that direction. If the grip is strong then the velocities of bat and ball in that direction will become equal while conserving momentum in that direction. Of course if you are considering rotational motion of the ball and/or the bat, then it is more complicated!

If the bat is NOT moving freely, but is just being moved by the hand and it keeps the same velocity during the collision, or if the bat is much heavier than the ball (both of these will be the case with pingpong bats), then it's just the same problem as the ball bouncing from a surface. You can use the equation in your drawing in your solution attempt. You only need to find vv.

You have to find the velocity of the ball relative to the bat, Then find the components of this velocity parallel to and perpendicular to the surface, And then flip the perpendicular component, and finally add the speed of the bat to the ball speed again to get the velocity of the ball relative to the earth.